Just a question to the OP, neither TK codeshares FRA-LAX or ZRH-LAX; neither LX/LH codeshares IST-FRA or IST-ZRH on TK; neither LX/LH codeshares IST-ACC on TK. I am not sure about how but which airline is issuing a single ticket for the routing ACC-IST-ZRH/FRA-LAX in your case? The routing could be complicated for a 13-year-old traveling alone and he/she might need to go to transfer desks as probably the agents in ACC would not be able to issue the boarding passes for the transatlantic leg. It's also possible that during a misconnection, he/she wouldn't be provided a hotel as the legal age of staying in a hotel alone ( without parental permission and signature ) is 18 in most parts of the world.

The risk is up to you.